Вправи для повторення розділу 1 » 62

62. Спростіть вираз: (4/(x^2- 6x) – 2/(6- x) + 1) • (2/(x^2- 4) – 2/(x^3- 6x^2+12x-8)) = 1/(x^2- 4). 1. 4/(x^3- 6x) – 2/(6- x) + 1 = 4/(x(x-6)) + 2/(x-6) + 1 = (4+2x+ x^2-6x)/(x(x-6)) = (x^2- 4x+4)/(x(x-6)); 2. x³ – 6x² + 12x – 8 = (x – 2)(x² + 2x + 4) – 6x(x – 2) = (x – 2)(x² + 2x + 4 – 6x) = (x – 2)(x² – 4x + 4) = (x – 2)(x – 2)² = (x – 2)³; 3. 1/(x^2- 4) – 2/((x-2)^3 ) = 1/((x-2)(x+2)) – 2/((x-2)^3 ) = ((x-2)^2-2(x+2))/((x-2)^3 (x+2)) = (x^2- 4x+4-2x-4)/((x-2)^3 (x+2)) = (x^2- 6x)/((x-2)^3 (x+2)); 4. (x^2- 4x+4)/(x(x-6)) • (x^2- 6x)/((x-2)^3 (x+2)) = ((x-2)^2• x(x-6))/(x(x-6)(x-2)^3 (x+2)) = 1/((x-2)(x+2)) = 1/(x^2- 4).